Trigonometry by Matthew Stone

1. Folio Task – How tall is the …?
Scenario
You have been given the task to determine the approximate
height of several Westminster School “landmarks”, for
example the Chapel, the MMC, the oval gum trees, the SSC,
the oval goal posts, the flag poles…
You will do this by measuring:
 the angle of elevation to the top of the object with
your clinometer
 the ground distance from the clinometer to the base
of the object (where possible)
 the distance from the clinometer to the ground
Through the use of right-angled triangle trigonometry, you
should then be able to find the approximate height of your
chosen Westminster “landmark”.
Materials required:
 Clinometer, measuring tape
Purpose
To demonstrate your ability to:
 accurately apply the mathematical concepts and relationships that you have learned in class to explore a
mathematical model for the given data
 communicate your results and solutions.
A completed investigation should include:
 an introduction that outlines the problem to be explored, including its significance, its features, and the
context
 the method required to find a solution, in terms of the mathematical model or strategy to be used
 the appropriate application of the mathematical model or strategy, including
o the generation or collection of relevant data and/or information, with details of the process of
collection
o mathematical calculations and results, and appropriate representations
o the analysis and interpretation of results
o reference to the limitations of the original problem
 a statement of the results and conclusions in the context of the original problem

2. Task One
There is a problem with the Cloister!!!!
It is apparently not a rectangle and the builders have made a mistake. Mr Bousfield has said, “THE CLOISTERS IS A
RECTANGLE and my Year 9 students will prove it.
Using Pythagoras’s Theorem, determine if Mr Bousfield is correct.
Task Two
Choose a landmark where the perpendicular base is easily accessible and the actual height can be measured with
a tape measure. We will choose the protective handrail of the upstairs cloisters.
From two different points, measure the angle of elevation to the top of your chosen landmark and the horizontal
distance to the foot of your chosen landmark.
Using these measurements, calculate the height of your chosen landmark.
Determine the average of your two results.
Record your results in the table below.
Object Angle of elevation
Reading 1
Distance to object
Reading 1
Angle of elevation
Reading 2
Distance to object
Reading 2
Compare your result with the result obtained by using the measuring tape.
Calculate the difference between your answer and the correct answer and convert your answer to a percentage
error
Hint: %𝒆𝒓𝒓𝒐𝒓 =
𝒂𝒄𝒕𝒖𝒂𝒍 𝒆𝒓𝒓𝒐𝒓
𝒄𝒐𝒓𝒓𝒆𝒄𝒕 𝒉𝒆𝒊𝒈𝒉𝒕
× 𝟏𝟎𝟎%

3. Task Three
Choose a landmark where the perpendicular base is easily accessible.
From two different points, measure the angle of elevation to the top of your chosen landmark and the horizontal
distance to the foot of your chosen landmark.
Using these measurements, calculate the height of your chosen landmark.
Record your results in the table below.
Object Angle of elevation
Reading 1
Distance to object
Reading 1
Angle of elevation
Reading 2
Distance to object
Reading 2